Modelling and optimal control of the market of a telecommunications operator

Abstract

A South African GSM telecommunications market consisting of two incumbents and an entering third player, is modelled utilising a non-linear, system dynamics approach. The model calculates subscriber choice based on a calculated utility. The utility is used to obtain a probability which is fed into a Bass type differential equation relating the different states in the model to their time derivatives. The model encapsulates all the prominent postpaid price plans in the market, as well as five different demographic market segments. Model Predictive Control is used to synthesise a linear feedback controller which uses the observed market state to optimally determine a price time series for one of the operators’ products. The series will maximise Average Revenue Per User (ARPU) for the operator over the simulation time interval. Besides ARPU, the controller is also able to increase total revenue and minimise churn over the simulated interval for the optimising operator, and thus provides valuable decision support to the marketing management of such an operator.